Cartan geometry provides a rich formalism from which to look at various geometrically motivated extensions to general relativity. In this manuscript, we start by motivating reasons to extend the theory of general relativity. We then introduce the reader to our technique, called the quotient manifold method, for extending the geometry of spacetime. We will specifically look at the class of theories formed from the various quotients of the conformal group. Starting with the conformal symmetries of Euclidean space, we construct a manifold where time manifests as a part of the geometry. Though there is no matter present in the geometry studied here, geometric terms analogous to dark energy and dark matter appear when we write down the Einstein tensor. Specifically, the quotient of the conformal group of Euclidean four-space by its Weyl subgroup results in a geometry possessing many of the properties of relativistic phase space, including both a natural symplectic form and nondegenerate Killing metric. We show the general solution possesses orthogonal Lagrangian submanifolds, with the induced metric and the spin connection on the submanifolds necessarily Lorentzian, despite the Euclidean starting point. By examining the structure equations of the biconformal space in an orthonormal frame adapted to its phase space properties, we also nd two new tensor fields exist in this geometry, not present in Riemannian geometry. The rst is a combination of the Weyl vector with the scale factor on the metric, and determines the time-like directions on the submanifolds. The second comes from the components of the spin connection, symmetric with respect to the new metric. Though this eld comes from the spin connection, it transforms homogeneously. Finally, we show in the absence of Cartan curvature or sources, the conguration space has geometric terms equivalent to a perfect fluid and a cosmological constant. We complete the analysis of this homogeneous space by transforming the known, general solution of the Maurer-Cartan equations into the orthogonal, Lagrangian basis. This results in a signature-changing metric, just as in the work of Spencer and Wheeler, however without any conditions on the curvature of the momentum sector. The Riemannian curvatures of the two submanifolds are directly related. We investigate the case where the curvature on the momentum submanifold vanishes, while the curvature of the configuration submanifold gives an effective energy-momentum tensor corresponding to a perfect fluid. In the second part of this manuscript, we look at the most general curved biconformal geometry dictated by the Wehner-Wheeler action. We use the assemblage of structure equations, Bianchi identities, and eld equations to show how the geometry of the manifolds self-organizes into trivial Weyl geometries, which can then be gauged to Riemannian geometries. The Bianchi identities reveal the strong relationships between the various curvatures, torsions, and cotorsions. The discussion of the curved case culminates in a number of simplifying restrictions that show general relativity as the base of the more general theory.

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<P> The Baie Verte Peninsula of Northern Newfoundland has a long history of mining and extraction. This area, which plays host to some of the oldest mines in the province, has a geologic setting favorable for Volcanogenic Massive Sulphides and is still considered to be one of the best exploration targets in Newfoundland. As less near-surface discoveries are made the requirement to look for deeper deposits becomes apparent and thus the role of geophysical modeling becomes progressively more important. This thesis examines the task of geologically supported geophysical modeling as a means to predict subsurface geological distributions and structure. Three case studies of modeling on the Baie Verte Peninsula are presented. A fourth study addresses the role of gamma attenuation for rapid density measurements in building physical property databases to be used as modeling constraint. </p> <P> A case study of the Betts Cove Ophiolite Complex along the western margins of Notre Dame Bay demonstrates the use of magnetic modeling to provide insight into the 3D nature of an area of previously significant ore extraction. While prior models have interpreted this feature to consist of a series of imbricate thrust slices, this new model suggests that the Betts Cove Ophiolite Complex is a doubly plunging syncline segmented by a several normal and high angle reverse faults. On a larger scale, this segmentation comprises a half-graben structure responsible for the morphology of Notre Dame Bay. Supported by petrophysics and a detailed structural dataset 2D forward geophysical models form the basis in the construction of a 3D geologic model of the Betts Cove Ophiolite and its cover series. </P> <P> An alternative approach to the conventional method of density measurement is presented in chapter three. Modifying an industrial gamma-gamma meter, a portable device has been constructed capable of providing rapid density measurements on bore-core. The device can be calibrated using a suite of metal alloy standards. It is possible to derive secondary empirical calibration based on a one-to-one gamma-gamma to specific gravity technique correlation. This study is one of only a very small fraction implementing this technology in an ocean-floor hard rock geologic setting. </p> <p> The second modeling case study focuses on the Rambler property in the upper Pacquet Harbour Group of the central Baie Verte Peninsula. The Rambler rhyolite is a felsic dome feature within the upper portions of an incomplete ophiolite. Ore deposits are found in association with contact between the felsic volcanics of the rhyolite and the mafic volcanic cover. 3D magnetic and gravity inversions are performed implementing the University of British Columbia Geophysical Inversion Facility's (UBC-GIF) code. A large physical property database has been constructed and used in the development of a reference model of known geologic distributions. The subsurface distribution of the Rambler rhyolite has been revealed through gravity inversions while additional structural information has been provided from magnetics. The results demonstrate the strengths of including geologic constraint within the inversion process and the ability of geophysical inversions to supplement and support current understanding and exploration techniques </p> <p> In the final case study, modeling is performed on a broader perspective in order to provide a regional geologic framework of the Baie Verte Peninsula. 2D forward models of magnetics and gravity profiles are constructed with multiple intersection points in order to enforce continuity in distribution and structure throughout. New geologic maps and a regional physical rock property database have been implemented in modeling while unconstrained 3D magnetic inversions are used as additional support. In addition to addressing such issues as regional basement morphology, the depth extent of the Cape Brule porphvry, and the nature of the Baie Verte Line, several prospective exploration targets have been revealed through this study. </p> / Thesis / Master of Science (MSc)

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